Equivalent Definitions of A Closed Set
In a topological space, a set is closed if and only if it coincides with its closure. Equivalently, a set is closed if and only if it contains all of its limit points.
This is not to be confused with a closed manifold.
Read more about this topic: Closed Set
Famous quotes containing the words equivalent, definitions, closed and/or set:
“Accountability in friendship is the equivalent of love without strategy.”
—Anita Brookner (b. 1938)
“Lord Byron is an exceedingly interesting person, and as such is it not to be regretted that he is a slave to the vilest and most vulgar prejudices, and as mad as the winds?
There have been many definitions of beauty in art. What is it? Beauty is what the untrained eyes consider abominable.”
—Edmond De Goncourt (1822–1896)
“Had I made capital on my prettiness, I should have closed the doors of public employment to women for many a year, by the very means which now makes them weak, underpaid competitors in the great workshop of the world.”
—Jane Grey Swisshelm (1815–1884)
“When parents fail to set appropriate limits, children may feel more vulnerable at night: the aggressive urges that have not been “tamed” by day may be terrifying to a small child alone in the dark.”
—Cathy Rindner Tempelsman (20th century)